Question

Which of the following is the general term for the sequence? -a, a^2, -a^3, a^4,...

Answer 1

Answer:

The answer would be $-a(-a)^{n-1}$.

Step-by-step explanation:

We can simply substitute the terms into this equation. Checking the 1st term, $-a(-a)^{1-1} = -a(-a)^{0} = -a(1) = -a$. Moving on to the second term, we see $-a(-a)^{2-1} = -a(-a)^{1} = -a(-a) = a^{2}$. And so on and so forth. We can see how the answer fluctuates between negative and positive, while gaining one more exponent every term, which fits with the sequence given. Therefore, the answer would be $-a(-a)^{n-1}$.

Hope this helped!